Finding an angle given an an angle of a loci.

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Sonal7

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I think this is a basic step but I cant understand it.

Q: The point P represents, the complex number Z that satisfies the equation .

[MATH] arg (z-1) -arg (z+3) =\frac {3}{4}\pi[/MATH]
Find the Cartesian equation of the locus.
1582921159331.png
I cant understand how they got the angle BCA. I can take it from there
 
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[MATH]Hint:[/MATH] Does this diagram help you? Notice the color of subtended angles and arcs.
1582929021904.png
 
I dont get it. Are you referring to the circle theorem where a the angle subtended at the centre is twice. Let me check.
 
I got it now, its the theorem. So the angle is as per the diagram !!! I was just dozing off and I could see it clearly. I wont bother with the explanation as its obvious.
 
pka said:
As I read the OP \(BCA\) is an arc of the circle. Therefore, \(C\) is a point of he circle and not its centre .
Is that not in the OP?
Click to expand...
In his diagram it is clearly showing that the [MATH]BDA[/MATH] is an arc and [MATH]C[/MATH] is the center.
 
Farzin said:
In his diagram it is clearly showing that the [MATH]BDA[/MATH] is an arc and [MATH]C[/MATH] is the center.
Click to expand...
You have badly misread his diagram. Either that are you do not understand this question.
arc.gif
TO Sonal7, please please try to clear up a clear misreading of your post.
Are you using the notation \(\widehat{ADC}~\&~\widehat{BCA}\) as two arcs of the same circle'?
But maybe those are angles?? If both are arcs then \(C\) cannot be the center of their circle. Is that correct??
I it is incorrect please tell us so. If it is correct then what is the center of their circle?
 
@pka: I think Farzin got it right. The notation used for both means angle, not arc (as is explicitly stated about BCA in the question), and (though not explicitly stated) C is the center of that arc. The picture in post #5 makes it clear what it means, and the fact that it works validates the interpretation.

@Farzin: I welcome you as a helper. I've seen some great work from you!
 
Dr.Peterson said:
@pka: I think Farzin got it right. The notation used for both means angle, not arc (as is explicitly stated about BCA in the question), and (though not explicitly stated) C is the center of that arc. The picture in post #5 makes it clear what it means, and the fact that it works validates the interpretation.

@Farzin: I welcome you as a helper. I've seen some great work from you!
Click to expand...
Thank you doc.
 
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